Solve for $g$. Give an exact answer. $12g=12\left(\dfrac23g-1\right)+11$ $g =$
Solution: We need to manipulate the equation to get $ g $ by itself. $\begin{aligned} 12g &= 12\left(\dfrac23g-1\right)+11 \\\\ 12g &= 8g-12+11~~~~~~~~~~\gray{\text{Distribute}}\\\\ 12g &= 8g-1~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 12g{-8g} &= 8g-1{-8g} ~~~~~~~~~~\gray{\text{Subtract 8g from each side}}\\\\ 4g&=-1 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{4g}{{4}}&= \dfrac{-1}{{4}}~~~~~~~~~~\gray{\text{Divide each side by 4}} \\\\ g &= {-\dfrac14} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ g= { -\dfrac14 }~~~~~~~~$ [Let's check our work!]